Relativistic Roche-Riemann problems around a black hole

Abstract

Based on a framework of the hydrodynamics for a fluid star of mass m orbiting a Kerr black hole of mass M ≫ m, relativistic Roche-Riemann ellipsoids for incompressible fluids are considered. It is found that in the relativistic Roche-Riemann limit for the irrotational Roche-Riemann ellipsoid moving at the innermost stable circular orbit around Kerr black holes, the angular velocity, Ω, becomes Ω2 ≃ 0.063637 πρ. We also argue implications of present results on the final fate of black hole-neutron star binary systems.